Comparative analysis of disease modelling for health economic evaluations of systemic therapies in advanced hepatocellular carcinoma

Background The objective of this study was to systematically analyse methodological and structural assumptions utilised in model-based health economic evaluations of systemic advanced hepatocellular carcinoma (HCC) therapies, discuss the existing challenges, and develop methodological recommendations for future models in advanced HCC. Methods We performed literature searches using five databases (Embase, PubMed, Web of Science, Econlit, and CNKI) up to December 4, 2022. Technology appraisals from Canada, England, Australia, and the United States were also considered. Model-based full economic evaluations of systemic advanced HCC therapies in English or Chinese met the eligibility criteria. The reporting quality was assessed by using the Consolidated Health Economic Evaluation Reporting Standards 2022 checklist. Results Of 12,863 records retrieved, 55 were eligible for inclusion. Markov model (n = 29, 53%) and partitioned survival model (n = 27, 49%) were the most commonly used modelling techniques. Most studies were based on health-state-driven structure (n = 51, 93%), followed by treatment-line-driven structure (n = 2, 4%) and combination structure (n = 1, 2%). Only three studies (5%) adopted external real-world data to extrapolate the overall survival or calibrate the extrapolation. Few studies reported the assumptions of transition probabilities. Utility modelling approaches were state-based (n = 51, 93%) and time-to-death (n = 1, 2%). Only 13 studies (24%) reported five types of model validation. Economic evaluation results of specific treatment strategies varied among studies. Conclusions Disease modelling for health economic evaluations of systemic therapies in advanced HCC has adopted various modelling approaches and assumptions, leading to marked uncertainties in results. By proposing methodological recommendations, we suggest that future model-based studies for health economic evaluation of HCC therapies should follow good modelling practice guidelines and improve modelling methods to generate reliable health and economic evidence.


Introduction
Hepatocellular carcinoma (HCC) raises a huge burden to societies and patients worldwide due to its high incidence, poor prognosis, and heavy costs.With approximately 906,000 diagnoses in 2020, primary liver cancer remains the 6 th most frequently diagnosed cancer, and there will be over annual 1,000,000 patients affected by liver cancer by 2025 [1,2].HCC comprises around 90% of liver cancer cases, being the major pathological type in liver cancer [2].A variety of risk factors for HCC have been proven, such as cirrhosis, chronic hepatitis B virus or hepatitis C virus infection, type 2 diabetes, obesity, non-alcoholic steatohepatitis, and heavy alcohol intake [2][3][4][5].
HCC progress rapidly, and most patients are diagnosed in an advanced stage.Although the emerging systemic therapies such as immune checkpoint inhibitors (ICIs)-based therapies have significantly improved the clinical outcomes in advanced HCC, the medical utilisation, productivity loss, and long and poor prognosis owing to the disease have brought a substantial economic burden to HCC patients and payers [6][7][8].The costs of HCC are forecasted to exceed US$500 million and JPY 607.2 billion annually in the United States (US) and Japan [9,10].Therefore, value evaluations integrating clinical effectiveness and costs are critical in determining cancer therapies.Health economic evaluations are needed to estimate the costeffectiveness of HCC therapies.
However, health economic evaluations of HCC therapies face methodological challenges.Likhitsup et al. [11] conducted a focused review of cost-effectiveness and economic burden of surveillance and treatment in HCC before January 2019.Although they mainly concluded that several surveillance treatment modalities for HCC were cost-effective, they expressed concerns about the lack of descriptions of assumptions and approaches of modelling, insufficient uncertainty analysis, and improper evidence synthesis.As the decisions concerning assumptions employed and methods taken in health economic evaluations will impact the eventual decision model-based estimates, it demands more rigorous methodological reconsiderations for health economic evaluations of advanced HCC treatments [11].
Therefore, we aimed to comprehensively investigate the approaches used in model-based health economic evaluations of systemic therapies in advanced HCC, discuss the existing challenges in the adopted model approaches and assumptions, and develop methodological recommendations for future advanced HCC models.

Data extraction
One author (HZ) conducted the data extraction, with two other authors (YX and XC) verifying all the extracted information.Data elements consisted of the following aspects: first author, publication year, location, base case population, study design, treatment strategies, outcomes of economic evaluations, modelling technique, model structure, health states, progression, time horizon, cycle length, validation efforts, sensitivity analyses, clinical data source, time-toevent distributions, transition probabilities, study perspective, utility modelling approach, disutility, cost scope, and discount rates.assessed the model specifications and described the quality of models critically in technology appraisals (TAs), further description of appraisal quality was not conducted in this review.

Search results
Searches from databases and websites of HTA agencies yielded 12,863 studies.After removing duplicates, 9,435 records were screened according to titles and abstracts, which resulted in 434 remaining to be assessed for the full text.In full-text screening, 379 studies were excluded owing to the absence of a decision analysis model or systemic therapy for HCC.Finally, 55 studies (45 publications and 10 TAs) met the eligibility criteria (Fig 1), of which 10 appraisal documents comprising company submissions and all relevant evaluations (e.g., Evidence Review Group reports) were identified from pan-Canadian Oncology Drug Review (pCODR, n = 5) and NICE (n = 5).

Quality assessment
The quality of included publications was described as the study-level quality scores in Table C in S1 Appendix.The percentage of each CHEERS item correctly reported is shown in Fig 2 .Reporting quality scores varied from 57% to 86%.One publication (2% of all publications), 40 publications (89%), and four publications (9%) scored < 60%, 60%-80%, and � 80%, respectively (Table C in S1 Appendix).Some items were not often appropriately reported (Fig 2).Thirty-two publications (71%) did not report the effectiveness measurement decision and thirty-seven (82%) did not characterize the heterogeneity.No publication followed a health economic analysis plan, engaged with patients and others in the research design, and characterized the distributional effects in the results.No study was excluded after the quality assessment since the objective of this review was to comprehensively summarize the modelling methods of systemic therapies in advanced HCC.

Economic evaluation results
Economic evaluation results of the similar or same treatment settings for advanced HCC varied among studies (Tables D and E  Of the Chinese studies including first-line treatment with donafenib, all but one showed improved cost-effectiveness in donafenib in comparison with sorafenib and lenvatinib [20][21][22], whereas the other study considered that donafenib was not a cost-effective strategy compared to sorafenib with an ICER of US$41,081.52/QALYgained (willingness-to-pay threshold of US$10,499.74-31,499.23/QALY,2020 values) [23].Regarding initial treatment with sintilimab plus bevacizumab biosimilar, one Chinese analysis revealed that it lacked cost-effectiveness when compared with sorafenib (ICER US$51,877.36/QALYgained), lenvatinib (ICER US $56,890.35/QALYgained), and donafenib (ICER US$66,487.88/QALYgained, willingness-topay threshold of US$33,521/QALY, 2020 values) [22], although the other four analyses showed a cost-effective profile of sintilimab plus bevacizumab biosimilar in China [24][25][26][27].For other treatment strategies, significant differences in results were also observed among studies, for which the reasons were probably that different modelling approaches and assumptions were adopted.

Decision model characteristics
Table 3 and Tables F and G in S1 Appendix summarised the main methodological characteristics of included decision models consisting of modelling technique and structure, time horizon, cycle length, discounting, clinical effectiveness inputs, utility and cost inputs, sensitivity analyses, and validation efforts.Summary of included decision models.Table 3 provided an overview of the general characteristics of included decision models.Markov model (n = 29, 53%) and partitioned survival model (n = 27, 49%) were the most commonly used modelling techniques for systemic therapies in advanced HCC.Two studies (4%) investigated both approaches to explore structural uncertainty [42,43].One study (2%) from the US did not detail the technique used [54].
Concerning model structure, most studies were based on a core structure of advanced HCC defined by a disease pathway of traditional three health states: progression-free survival (PFS), progressive disease (PD), and death (n = 51, 93%).Of these models, four divided the PD state into continuous first-line treatment and off-first-line treatment after progression [15,16,48,60], one model added a state in PFS to reflect intolerance (adverse events) [51], one model      involved an additional recurrence-free survival (RFS) state [39], and one merged PFS and PD into one disease state [31].The disease progression in the health-state-driven model structure was that (Fig 3), in general, advanced HCC patients receiving systemic therapy started in the PFS state, following which they could stop treatment due to intolerance (adverse events).Before transitioning to PD, patients could experience an additional state of RFS.Once in the PD state, patients could either continue or stop previous treatment.Also, the transition to death could happen from any health state in the model.Two studies (4%) employed a treatment-line-driven structure in which patients could progress from receiving first-line treatment to second-line treatment and later switch to death (Fig 4) [28,29].One study (2%) applied a combination structure of health-state and treatmentline-driven ones, allowing nine health states for two lines of treatment [49].Within the model, patients began by receiving first-line treatment, and they could progress to any state of the first-line treatment regardless of whether toxicity occurred or not.After first-line discontinuation owing to toxicity or progression, patients could move to the second-line treatment.There was no subsequent-line treatment if patients experienced second intolerance or progression.Similarly, death could occur at any point in the model (Fig 5).
Additionally, only one study used external RWD to extrapolate the OS [33].In Chiang et al., survival curves were parametric in base-case analysis; however, the Surveillance, Epidemiology, and End Results (SEER) data were utilized to extrapolate the OS after 17 months in the atezolizumab-bevacizumab arm in scenario analysis [33].In terms of calibration of survival extrapolation, in NICE TA 474 and Saiyed et al., authors used external RWD of the matched GIDEON data and Australian Cancer Database to calibrate the OS extrapolations [47,60].
Generally, in advanced HCC models, transition probabilities (n = 29, 53%) in Markov models and survival functions (n = 27, 49%) in partitioned survival models informed HCC progression (i.e.distribution of patients in each state in each cycle, Table 4).Concerning the transition probabilities, several approaches were adopted for those calculations in the included Markov models.Parametric survival modelling was the most frequently used method (n = 13, 24%), while model calibration (n = 2, 4%) [41,56] and non-parametric count method (n = 1, 2%) [48] were also involved.In order to estimate the time-dependent transition probabilities in cancer models, the assumptions of parametric distributions for survival data were usually required.The Weibull distribution was often chosen since it belonged to the continuous probability distribution, of which the survival function parameters were then employed for deriving transition probabilities [70].Five models using parametric survival modelling methods reported the following formulas of transition probabilities based on Weibull distribution: λ = scale parameter of Weibull distribution, γ = shape parameter of Weibull distribution, u = cycle length [30]; on this basis, a simplified formula was derived: 34,57,59].The remaining 24 Markov models did not clarify how the transition probabilities were obtained.Furthermore, for reducing calculation, the probability from PFS state to death was commonly assumed to be the natural mortality in most models, and the constant transition probabilities over time were even assumed in 10 ones [17-19, 34, 41, 45, 48, 56, 57, 59].
Utility and cost inputs.Table G in S1 Appendix presented the utility and cost inputs of identified models.Two approaches were reported for utility modelling (Table 5).A total of 51 studies (93%) adopted the state-based approach, whereas only one study (2%) modelled utilities through the proximity to death approach in base-case analysis [63].The studies using a state-based approach defined the utilities of PFS and PD states.One study pursued the following time-to-death intervals when applying this approach: > 30 weeks, > 15 to � 30 weeks, > 5 to � 15 weeks, and � 5 weeks before death [63].
The utilities of 0.76 and 0.68 used for PFS and PD states were the most common values for advanced HCC models (n = 27, 49%), and the pCODR Review Team considered these utility values more appropriate for the advanced HCC patient population [66].In 17 studies (31%), utility values were equivalent across the treatment arms, since there was a lack of exploration for differentiation possibility or consideration for disutility of adverse events in base-case or scenario analysis.Thirty-three studies (60%) assumed different utilities across the treatment arms by means of applying the disutilities of adverse events or differentiating the values of base utility.Additionally, one study (2%) also used age adjustment to utility values [64].
With regard to the sources of utility, 33 studies (60%) generated the utility values only from published literature.Fifteen studies (27%) applied the EQ-5D utilities obtained in the trials, of which one (2%) used the adjusted EQ-5D data from REFLECT to reflect Japan-specific utilities [36].Two studies (4%) involved the FACT-Hep data collected during clinical trials [45,60] and one (2%) reported the use of SF-6D data from Chinese HCC patients [48].

Discussion
This systematic literature review was the first study to evaluate disease modelling for health economic evaluations of systemic therapies in advanced HCC, focusing on methodological characteristics and key challenges of decision models.This systematic analysis comprised modelling technique and structure, time horizon, cycle length, discounting, clinical effectiveness inputs, utility and cost inputs, sensitivity analyses, and validation efforts.It revealed wide variations of economic evaluation results in advanced HCC modelling studies, which could be attributed to marked differences in the adopted model approaches and assumptions.Consequently, the considerations and selections of (1) model structure and technique, (2) time horizon, cycle length and discounting, (3) clinical effectiveness inputs, (4) utility and cost inputs, (5) sensitivity analyses and validation efforts, (6) patient characteristics, (7) duration of treatment, and (8) switch, were discussed in this section.The key recommendations proposed across the discussion are summarized in Table 6.

Model structure and technique
Most advanced HCC models used the traditional three health states of PFS, PD, and death to define their structures.However, applying such a structure would be problematic if the models were to consider conditional outcomes and treatment sequences.Most health-state-driven models accounted for all subsequent therapy in a PD state, implying patients received the same treatment after disease progression until death.This assumption did not reflect the clinical practice, and stronger ones were required for modelling downstream treatments.Thus, combining treatment-line-driven structure could be more realistic in simulating treatment pathways.
In the economic evaluations for oncology therapies, the dominant decision analysis models involved Markov and partitioned survival models, which were the only techniques for modelling the health and economic outcomes in included publications and TAs.However, when considering multiple adverse events and different treatment lines, a number of assumptions and model states were required, which would contribute to greatly untransparent and complex models.Therefore, it is more suggested to adopt patient-level modelling techniques including patient-level long short-term memory or discrete event simulation.Specially, discrete event simulation could provide flexibility in the fields of event timing, competing event handling, and model structure, leading to a preferable reflection of clinical practice.Patient-level techniques, however, were widely regarded as more time consuming and complex, and there was lack of guidance for model implementation.

Time horizon, cycle length, and discounting
Time horizons, cycle lengths, and discount rates differed between studies in this review.NICE guideline for TA recommends that the health economic model should adopt a sufficiently long time horizon to evaluate all significant differences in benefits and survivals between compared treatments [71].When alternative treatments impact outcomes or costs that persist throughout a patient's remaining life, a horizon of lifetime is usually required [71].In addition, the cycle length is generally accepted to be consistent with the treatment cycle.The annual discount rate changes over time and across jurisdictions, such as currently 3.5% recommended for UK [71], 5% for China [72], and 5% for Australia [73].

Clinical effectiveness inputs
The research community seemed to hardly get access to IPD from industry-funded trials, which led to limitations in decision making, structure employed, and methods used.OS served as the critical parameter impacting on economic evaluation results, but its extrapolation was filled with challenges for the treatments associated with sustained responses.It was difficult to accurately model the OS only adopting parametric distributions based on trial data, since a plateau of the tail occurred in the sustained response-related OS curve.In accordance with guidelines of HTA, the extrapolation and plausibility of long-term survival can be informed and assessed using external data [74].The external and internal validity are standardly balanced through trade-off between adopting external data and trial data-based parametric distribution.Importantly, the treatment options and patient population of external data should be assessed to coincide with that in the trial.We found only one study using SEER data for the extrapolation of OS in a pessimistic scenario [33].Moreover, calibrating the extrapolation based on external data becomes a good practice.We identified two studies using RWD (i.e. the matched GIDEON data and Australian Cancer Database) for calibration of their parametric OS extrapolations [47,60].

Reporting good practices
To improve reporting good practices, especially for selection of extrapolation methods, decisions on measurement of effectiveness, identification of parameters used in sensitivity analysis and assumption of distributions or uncertainty for these parameters

Modelling good practices
To improve modelling good practices, especially for definition of model structure that reflects the clinical practice, selection of modelling technique that matches the structure, explanation of time-to-event parameters (including distribution parameters and transition probabilities), selection of approach to utility modelling, presentation of methods of sensitivity analyses, utilization of model validation

Specific recommendations
Model When adopting state transition models, there was a rising need for justifications of transition probabilities that were used between states.The most frequently used approach for cancer models in estimating transition probabilities was parametric survival modelling methods [75].The maximum likelihood estimation was typically used during parametric survival functions fitting to IPD for estimations of survival function parameters, such as the shape and scale parameters of the Weibull distribution, which were employed to derive transition probabilities later.The transition probabilities of the interest events were defined as: S = survivor function, (t i-1 , t i ) = time interval [75].
In fact, most Markov models of systemic therapies in advanced HCC did not describe the calculation method or formula derivation process for transition probabilities, which could be associated with the major uncertainty and become one of the concerns in future models.

Utility and cost inputs
Utility inputs significantly affect economic evaluation results.Given the utility models, the data quality has an important impact on the approach adopted.For instance, there should be enough patient samples in each proximity-to-death interval and the utility value should be validated for its face validity, if the time-to-death approach is taken.In NICE TA 666, the decision model defined the utilities based on time-to-death intervals, because this approach could drive a more refined division of health states compared with the state-based approach [63].However, the evidence review groups from NICE did not clearly favor time-to-death or state-based utility models, and thus further evidence should be needed.
It was also worth noting that adverse events were generally served as an important part of the cost and utility in a treatment cycle, but seldom involved as separate events.Consequently, the costs of managing adverse events and disutilities of adverse events deserve attention and research in advanced HCC models.

Sensitivity analyses and validation efforts
The studies provided limited details on the methodologies of sensitivity analyses, even though more than 90% of them reported one-way or probabilistic sensitivity analyses.Particularly in probabilistic analysis, identifying included parameters and quantifying uncertainty surrounding them were extremely important; otherwise, interpreting adopted confidence intervals was unlikely.
For only 13 studies, five types of validation were used in the publication, mainly being face validity of models and assumptions judged by experts.The validity and outcomes of models could be questioned if being a lack of model validation.Thus, future health economic models for advanced HCC need to better utilize the existing frameworks to reflect the validity of the models [76,77].

Patient characteristics
The differences in epidemiological and physiological characteristics, including age, sex, ethnicity, Eastern Cooperative Oncology Group performance status, etiology of disease, Child-Pugh class, Barcelona Clinic Liver Cancer (BCLC) stage, extrahepatic spread of disease, macrovascular invasion, alpha-fetoprotein concentration, and previous treatment history in patients diagnosed as advanced HCC, could result in needs for modelling which is more associated with these differences.Actually, the identified models rarely took this into consideration, and thus future studies were required to consider the modelling being more sensitive to the differences of patient characteristics, and to categorize advanced HCC patients into different appropriate models based on different patient characteristics and evaluate them separately.

Duration of treatment
There was an ongoing challenge to determine the optimal duration of systemic therapies for advanced HCC in clinical practice.Duration of treatment was modelled mostly adopting time to discontinuation and PFS.The data of time to discontinuation would be preferable against that of PFS, when the Kaplan-Meier curve or IPD of time to discontinuation were available.Otherwise, PFS could be considered as a proxy of time to discontinuation.However, given that patients might continue on previous treatment after disease progression, this approach might underestimate the treatment duration likely presented in clinical practice.Most advanced HCC models did not define the measure of treatment duration, and this concern should be solved in the future.

Switch
Treatment switching due to disease progression or intolerance commonly occurred in the trials for advanced HCC and its pattern, namely proportion of switching and treatments, needed to be reflective of clinical practice in the analyzed jurisdiction.The majority of identified studies involved treatment switching, yet few presented the selected adjustment methods and rationales, implying poor quality for reporting the switching adjustment implementation [78].A technical support document from NICE [79] and a publication [78] provided definitions and applications of various switching adjustment methods such as inverse probability of censoring weights and iterative parameter estimation algorithm.Future studies should employ the most suitable adjustment method matching the corresponding assumptions and visually comparing adjusted and actual OS curves [78,79].

Limitations
There were certain limitations in this review.Firstly, owing to the absence of a more appropriate alternative, we used the CHEERS 2022 checklist that was not designed to assess publication quality.The CHEERS checklist scores were not generally reflective of the modelling quality, since reporting on items did not actually represent that they were appropriately implemented.Secondly, some extracted data lacked definite data sources, model structures, assumptions, and adopted methods, and readers and researchers might not agree with these categorizations.To reduce such impact to the utmost extent, two other authors verified all the extracted information.

Conclusions
Disease modelling for health economic evaluations of systemic therapies in advanced HCC has adopted various modelling approaches and assumptions, resulting in marked differences in economic evaluation results.It implied that there had been much uncertainty associated with cost-effectiveness of systemic therapies for HCC.By proposing methodological recommendations, we suggest that future model-based studies for health economic evaluation of HCC therapies should follow good modelling practice guidelines and improve modelling methods to generate reliable health and economic evidence, especially in definition of model structure that reflects the clinical practice, selection of modelling technique that matches the structure, explanation of time-to-event parameters, selection of approach to utility modelling, presentation of methods of sensitivity analyses, and utilization of model validation.

Table 6 . Summary of key recommendations for disease modelling for health economic evaluations of systemic therapies in advanced HCC.
structure To distinguish different treatment lines in the model structure to simulate more realistic treatment pathways Modelling technique To adopt the patient-level modelling technique if available which can provide flexibility in the fields of event timing, competing event handling, and model structure Patient characteristics To evaluate the differences of patient characteristics, and to consider the modelling being more sensitive to these differences Duration of treatment To model duration of treatment using time to discontinuation, when the Kaplan-Meier curve or IPD of time to discontinuation are available Treatment switching To employ and define the most suitable adjustment method matching the corresponding assumptions, and to compare adjusted and actual OS curves visually Abbreviations: HCC, hepatocellular carcinoma; IPD, individual patient data; OS, overall survival.https://doi.org/10.1371/journal.pone.0292239.t006